Superflares are very strong explosions observed on stars with energies up to ten thousand times that of typical solar flares. The stars in this class satisfy conditions which should make them solar analogues, and would be expected to be stable over very long time scales. The original nine candidates were detected by a variety of methods. No systematic study was possible until the launch of the Kepler satellite, which monitored a very large number of solar-type stars with very high accuracy for an extended period. This showed that a small proportion of stars had violent outbursts, up to 10,000 times as powerful as the strongest flares known on the Sun. In many cases there were multiple events on the same star. Younger stars were more likely to flare than old ones, but strong events were seen on stars as old as the Sun.